Quasispecies Evolution in the Strong Selection Limit
        Joachim Krug, C. Karl and T. Halpin-Healy
        Physics Dept. University of Essen 
        D-45117 Essen, Germany 

 
The close formal similarity between the discrete time version of quasispecies evolution in a rugged fitness landscape [1] and the problem of  directed polymers in the presence of columnar disorder has been noticed for some time [2,3]. In the strong selection/zero temperature limit the population resides at a single point of sequence space at any given time, and moves towards the global fitness optimum through a succession of evolutionary
jumps between local optima. The talk will present numerical and analytic results for the statistics of lengths and durations of these evolutionary histories, and contrast them with the behavior of simple adaptive walks [4], directed polymers on hypercubic lattices [2] and the theory of records [5].

[1] M. Eigen, J. Mc Caskill and P. Schuster, Adv. Chem. Phys. 75, 149 (1989).
[2] J. Krug and T. Halpin-Healy, J. Phys. I France 3, 2179 (1993).
[3] S. Gallucio, Phys. Rev. E 56, 4526 (1997).
[4] H. Flyvbjerg and B. Lautrup, Phys. Rev. A 46, 6714 (1992).
[5] W. Feller, Introduction to Probability Theory and Its Applications
(Wiley, New York 1971).

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